# Some new formulas for pi

### (28 pages)

Abstract. We show how to find arbitrarily fast convergent series expansions for \pi of the form \pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}, where S(n) is some polynomial in n (depending on m,p,a). We prove that there exist such expansions for m=8k, p=4k, a=(-4)k, for any k, and give explicit examples for such expansions for small values of m, p and a.

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